1
m-Hydroxybenzoic Acid: Quantifying
Thermodynamic Stability and Influence of Solvent on
the Nucleation of a Polymorphic System
Michael Svärd† and Åke C. Rasmuson*‡†
†) Department of Chemical Engineering and Technology, KTH Royal Institute of Technology,
Stockholm, Sweden
‡)
Department of Chemical and Environmental Science, Solid State Pharmaceutical Cluster, Materials and Surface Science Institute, University of Limerick, Limerick, Ireland
*) To whom correspondence should be addressed. E-mail: [email protected]
OPEN ACCESS VERSION DECLARATION
This is the accepted version of the following article:
Svärd, M. and Å.C. Rasmuson; Cryst. Growth Des. 13(3), 1140-1152 (2013), which has been published in final form at:
http://pubs.acs.org/doi/abs/10.1021/cg301483x
ABSTRACT: Nucleation of m-hydroxybenzoic acid crystals in different pure solvents has been investigated, and the thermodynamic interrelationship between two polymorphs analysed. The melting properties and specific heat capacities of both polymorphs have been determined by differential scanning calorimetry and the solubility in several solvents at different temperatures measured gravimetrically. Absolute values of the Gibbs free energy, enthalpy and entropy of fusion, and the activity of the polymorphs have been determined as functions of temperature. It is established that the polymorphs are monotropically related, with differences in enthalpy and Gibbs free energy of approximately one kJ/mol at room temperature. In a total of 539 nucleation experiments, in six solvents and with different cooling rates, the visible onset of nucleation was recorded and the nucleating polymorph isolated. It is found that the degree of supersaturation required for nucleation and the polymorphic outcome depend strongly on the solvent. The metastable polymorph is kinetically favoured under all evaluated experimental conditions, and for most of the conditions it is also statistically the most probable outcome. Nucleation of the stable polymorph is increasingly promoted in solvents of increasing solubility. It is shown how this can be rationalized by analysis of solubility and rate of supersaturation generation.
Keywords: calorimetry, chemical potential driving force, crystallization, metastable zone,
nucleation, polymorphism, solubility, solvent, supersaturation, thermodynamic stability, solid-state activity, van’t Hoff enthalpy of solution.
2
I
NTRODUCTIONIn several branches of the chemical industry, an important consideration in the design and optimization of many processes is the common phenomenon of polymorphism, the possibility of multiple different crystal structures of the same compound. This is especially true in the pharmaceutical industry, as polymorphs can have significantly different solubility and dissolution rate, leading to different bioavailability, and there are strict regulations requiring process control with respect to possible polymorphism of APIs and excipients1. In addition, polymorphs can form the basis for
important intellectual property rights. A key to controlling the polymorphic outcome in crystallization lies in the initial step, primary nucleation. There is no generally accepted theory that is able to satisfactorily describe the nucleation process. Which polymorph will nucleate depends on the thermodynamic stability relationship as well as on kinetic parameters such as rate of supersaturation generation2, and – not least – solvent. The influence of the solvent is complex, and depending on the
system studied has been attributed to an influence on the aggregation of molecules in solution into units such as dimers3-5, and to selective adsorption to certain crystal faces, affecting relative growth rates6, 7.
Substituted benzoic acids are chemically simple, yet to the pharmaceutical industry important molecules, many of which have been found to exhibit polymorphism. Recently, the polymorphism of the substance o-aminobenzoic acid which has three known structures was thoroughly investigated8, as was the singular polymorphism of the compound m-aminobenzoic acid, which has at least five polymorphs, three of which are zwitterionic9, 10. Out of the three monohydroxybenzoic acids, the solubility of which we have evaluated in several solvents11-13, the ortho-substituted isomer has no reported polymorphs, whereas the meta and para-isomers both have two14. In the present contribution, the thermodynamic properties and the nucleation behaviour of the two known polymorphs of m-hydroxybenzoic acid (mHBA, Figure 1) are investigated. The crystal structures of both polymorphs are known15. The structure of the thermodynamically stable polymorph at room temperature12, henceforth termed form I, contains the carboxylic acid dimer motif packed in the common herring-bone pattern, whereas that of the metastable polymorph, form II, features intermolecular hydrogen bond chains involving alternate COOH and OH-groups, creating layers of ribbons where the non-polar regions of neighbouring ribbons interact through van der Waals’ forces. In a previous contribution we gave an account of experiments probing the influence of the thermal and structural history of solution on the nucleation of mHBA polymorphs in ethyl acetate solution16. Here, we report a quantitative investigation into the thermodynamic properties of both polymorphs, and into the nucleation behaviour in five different solvents. Solubility data in some solvents published previously12 is complemented by calorimetric data and solubility data of both polymorphs in additional solvents, and is used to determine the thermodynamic relationship between the polymorphs. The principal aim is to investigate how changes in experimental conditions affect the nucleation kinetics of the two polymorphs. We have endeavoured to pay proper attention to the stochastic nature of nucleation, especially its effects on the polymorphic outcome.
3
T
HEORYThermodynamic stability
A measure of the thermodynamic stability of a solid phase at a given temperature is the activity of the solute molecules in a solution at equilibrium with the solid, aeq. If we adopt the standard convention
in chemical engineering of choosing the same reference state for the activity of the pure solid as for the solute in solution, viz. the pure compound in liquid state at the same temperature – in effect a supercooled melt – then the activity of the solid17 becomes:
ln 𝑎𝑆 = ln 𝑎𝑒𝑞 = 𝜇𝑆−𝜇𝐿 𝑅𝑇 = −∆𝐺𝑓 𝑅𝑇 = ∆𝑆𝑓 𝑅 − ∆𝐻𝑓 𝑅𝑇 (1)
where ΔGf, ΔHf and ΔSf denote the Gibbs free energy of fusion and its enthalpic and entropic
components. Values of these properties at any given temperature can be obtained from the corresponding values at the melting temperature through integration of the heat capacity difference between the pure liquid state and the solid state, ΔCP:
∆𝐻𝑓 = ∆𝐻𝑓(𝑇 𝑚) + ∫ ∆𝐶𝑃 𝑑𝑇 𝑇 𝑇𝑚 (2) ∆𝑆𝑓 =∆𝐻𝑓(𝑇𝑚) 𝑇𝑚 + ∫ ∆𝐶𝑃 𝑇 𝑑𝑇 𝑇 𝑇𝑚 (3)
Approximating the functional form of ΔCP with a linear equation with two parameters to be
determined for each polymorph:
∆𝐶𝑃 = 𝑞 + 𝑟(𝑇𝑚− 𝑇) (4)
leads to the following expressions for the activity of a solid phase, the Gibbs free energy of fusion and its components:
ln 𝑎𝑆 = ∆𝐻𝑓(𝑇𝑚) 𝑅 ( 1 𝑇𝑚− 1 𝑇) − 𝑞 𝑅(ln 𝑇𝑚 𝑇 − 𝑇𝑚 𝑇 + 1) − 𝑟 𝑅(𝑇𝑚ln 𝑇𝑚 𝑇 − 𝑇𝑚2 2𝑇+ 𝑇 2) (5) ∆𝐺𝑓= −𝑅𝑇 ln 𝑎𝑆 = ∆𝐻𝑓(𝑇𝑚) (1 − 𝑇 𝑇𝑚) + 𝑞 (𝑇 − 𝑇𝑚− 𝑇 ln 𝑇𝑚 𝑇) + 𝑟 ( 𝑇2 2 − 𝑇𝑚2 2 −𝑇𝑇𝑚ln 𝑇 𝑇𝑚) (6) ∆𝐻𝑓 = ∆𝐻𝑓(𝑇𝑚) + 𝑞(𝑇 − 𝑇𝑚) − 𝑟 2(𝑇 − 𝑇𝑚) 2 (7) 𝑇∆𝑆𝑓=𝑇∆𝐻𝑓(𝑇𝑚) 𝑇𝑚 + 𝑞𝑇 ln 𝑇 𝑇𝑚+ 𝑟 (𝑇𝑇𝑚ln 𝑇 𝑇𝑚− 𝑇 2+ 𝑇𝑇 𝑚) (8) Nucleation
For a solution which is brought to a state of supersaturation there will be a thermodynamic driving force for nucleation and growth of crystals, equal to the difference in chemical potential between that of the solute in the supersaturated solution, μ, and in a saturated solution at equilibrium with a pure crystal, μeq = μS: ∆𝜇 = 𝜇 − 𝜇𝑒𝑞= 𝑅𝑇 ln [ 𝑎 𝑎𝑒𝑞] = 𝑅𝑇 ln [ 𝑥 𝑥𝑒𝑞 𝛾 𝛾𝑒𝑞] ≅ 𝑅𝑇 ln [ 𝑥 𝑥𝑒𝑞] = 𝑅𝑇 ln 𝑠 (9)
The activity coefficient γ depends on x as well as T, but the ratio is often assumed to be close to unity. The classical theory of primary nucleation18-20 stipulates that nuclei are formed by monomers in solution aggregating into clusters having the structure of the bulk crystalline material. The cluster will become thermodynamically stable and able to grow into a crystal if its size exceeds a critical size where the total free energy gain overcomes the free energy cost of creating a phase boundary. The
4 steady-state rate of nucleation, J, is the product of the attachment frequency of molecules to a critical nucleus, f*, the equilibrium concentration of critical nuclei, C*, and the Zeldovich factor, Z, which
corrects for deviation from equilibrium, which, assuming spherical nuclei and monomer attachment controlled by volume diffusion, can be written as21, 22:
𝑓∗= 4𝜋𝑟∗𝜅𝐶𝐷 (10) 𝐶∗ = 𝐶 𝑛𝑠exp (− ∆𝐺∗ 𝑅𝑇) (11) 𝑍 = Δμ2 8𝜋𝑉𝑚√ 1 𝑅𝑇𝜎3 (12)
Eq 10 takes a slightly different form for a surface integration controlled process. Through the Einstein-Stokes equation the diffusion coefficient D is expected to depend on temperature and viscosity, and empirically it has been found to correlate to the solvent molar mass23. It can be argued that all molecules in a solution may serve as nucleation sites21, and hence the molar concentration of nucleation
sites in the system Cns may be approximated by the reciprocal of the solvent molar volume. Expanding
the expression for J using these and other22 approximations results in eq 13, applicable to steady-state primary, homogeneous 3D nucleation of spherical particles:
𝐽 ∝ 𝐶 ln 𝑠 𝜂𝑉𝑚,𝑠𝑜𝑙𝑣𝑒𝑛𝑡√ 𝑇3𝑀 𝑠𝑜𝑙𝑣𝑒𝑛𝑡 𝜎 exp (− 𝐴𝜎3 𝑇3𝑙𝑛2𝑠) (13)
E
XPERIMENTALW
ORK Materialsm-Hydroxybenzoic acid (mHBA, CAS reg. no. 99-06-9, purity >99%) was purchased from Sigma-Aldrich, and recrystallized once in methanol before use (vide infra). The following solvents were purchased from VWR: ethyl acetate (EtOAc, >99.8%), acetonitrile (MeCN, >99.8%) and 1-propanol (1-PrOH, >99.8%). Methanol (MeOH, >99.9%) was purchased from Sigma-Aldrich, and ethanol (EtOH, >99.7%) from Solveco. All organic solvents were used as obtained. Water used as solvent was deionised and filtered through a cellulose acetate (CA) membrane (pore size = 0.2 μm).
Polymorph identification and preparation
Figure 2. FTIR spectra of the two mHBA polymorphs: form I (red, upper) and form II (blue, lower).
FTIR spectroscopy has been used for the identification and characterization of the polymorphs of mHBA. A Perkin Elmer Spectrum One with an attenuated total reflectance (ATR) module equipped with a ZnSe-crystal window was used, with a scanning range of 650–2000 cm-1 and a resolution of 4 cm-1. The FTIR spectra of the two polymorphs are shown in Figure 2. Form I was prepared and
5 purified by dissolving purchased crystalline mHBA to saturation at 50 °C in ethanol, filtering the solution through Munktell grade 1002 filter paper, and cooling rapidly to 5 °C. Form II was prepared by dissolving recrystallized form I to saturation at 50 °C in ethyl acetate, filtering and cooling rapidly to 5 °C. The resulting crystals were filtered and dried at room temperature.
Solubility
The solubility of form I in ethanol and 1-propanol and of form II in water and 1-propanol was determined as described by Nordström and Rasmuson (2006)12. Solutions containing excess solid material, prepared in sealed 250 ml bottles agitated by PTFE-coated magnetic bars, were allowed to equilibrate by dissolution at different temperatures ranging from 10–50 °C. The temperature was controlled with a Julabo FP-50 thermostatic bath to within ±0.01 °C. Multiple solution samples were collected at each temperature with pre-heated syringes equipped with membrane filters (0.2 μm; PTFE or CA) and the sample mass recorded directly and after drying, with a precision of ±0.1 mg. FTIR was used to verify that form II crystals had not transformed in solution.
Thermal analysis
The melting temperature and associated enthalpy of fusion of both polymorphs of mHBA were measured with differential scanning calorimetry (DSC), using a TA Instruments DSC 2920 with hermetically sealed aluminium pans. A temperature ramp rate of 5 °C/min was used, and a cycle of repeated heating and cooling steps was employed. The instrument was calibrated according to standard procedure against the melting properties of indium and with a linear baseline correction. The isobaric, specific heat capacity (CP) of the pure polymorphs was determined with modulated DSC using
non-hermetic aluminium sample pans. A modulation period of 100 s and an amplitude of 1 °C were chosen, with an underlying constant heating rate of 3 °C/min following an initial 10 min isothermal step. The instrument was calibrated against the melting properties of indium, and the heat capacity signal was calibrated against a sapphire sample with three scans in the temperature interval -30–130 °C, using a linear calibration correction function. In all DSC runs, pans were selected so as to keep the difference in weight between sample pan and reference pan to within ±0.10 mg.
Nucleation experiments
Saturated solutions (with respect to the stable polymorph) prepared in 500 ml bottles at 50 °C were filtered into sealed 15 ml test tubes, agitated with PTFE-coated magnetic bars, using pre-heated syringes equipped with membrane filters (0.2 μm; PTFE or CA), in batches of 30 test tubes. Each batch was kept at an elevated temperature of 60 °C for 6 h, and then at 55 °C for another 6–10 h, in order to standardize the pre-treatment of solutions and minimize effects of solution history16, 24. The test tubes were then cooled at a constant cooling rate of either 3 °C/h or 10 °C/h. The visible onset of nucleation was recorded with a Sony HDR-XR200 high-resolution digital camcorder. This event invariably consisted of a transformation from clear to turbid solution, allowing the onset temperature to be determined visually to within an estimated accuracy of ±0.1 °C. As soon as sufficient crystal material had precipitated in a given test tube, the contents were filtered using Munktell grade 00A filter paper and dried in a ventilated fume hood until just dry (time depending on solvent and deposited amount). FTIR spectroscopy was then used for polymorph identification. All solution concentrations were verified gravimetrically.
R
ESULTS ANDD
ISCUSSIONThermodynamic stability relationship
The solubility of form I was determined in the range 10–50 °C with temperature increments of 5 °C in ethanol and 1-propanol. The solubility of form II was successfully determined throughout the full temperature range in water and at low temperatures in 1-propanol. Transformation into form I prevented further solubility measurement of form II. The collected solubility data is given in Table 1.
6 In order to allow extrapolation and interpolation of solubilities to different temperatures, an empirical three-parameter regression model given by eq 14 was fitted to the data in Table 1 as well as to solubility data in other solvents reported by Nordström and Rasmuson12, using the software Origin 6.1. The
functional form of eq 14 has been found to offer good robustness and accuracy in extrapolation to melting points25.
ln 𝑥𝑒𝑞= 𝐴𝑇−1+ 𝐵 + 𝐶𝑇 (14)
xeq is the mole fraction solubility and T the temperature in Kelvin. The coefficients A, B and C are
listed together with associated goodness of fit (2) in Table 2. Data for form II in 1-propanol was
excluded. The solubility regression curves are shown in Figure 3.
Table 1. Solubility of the Polymorphs of mHBA Given As Average Values Together With 95%
Confidence Limits, with the Number of Samples in Brackets
temperature solubility [no. of samples] given as g mHBA/kg solvent
[°C] form I form II
ethanol 1-propanol water 1-propanol
10 328.53 ± 1.99 [5] 221.82 ± 4.28 [4] 5.61 ± 0.21 [8] 254.54 ± 0.40 [4] 15 341.67 ± 3.49 [3] 231.06 ± 2.61 [4] 6.93 ± 0.36 [7] 269.91 ± 0.53 [4] 20 360.25 ± 0.65 [4] 242.92 ± 0.19 [4] 8.23 ± 0.11 [6] 281.44 ± 0.19 [6] 25 377.92 ± 0.27 [6] 257.87 ± 0.23 [6] 10.41 ± 0.17 [6] - 30 406.65 ± 0.37 [4] 276.14 ± 0.59 [4] 12.82 ± 0.26 [4] - 35 424.29 ± 0.58 [4] 291.84 ± 0.22 [4] 15.70 ± 0.27 [6] - 40 449.60 ± 0.65 [4] 310.60 ± 0.41 [4] 20.52 ± 0.56 [4] - 45 476.20 ± 0.13 [4] 330.66 ± 0.06 [4] 23.95 ± 0.86 [4] - 50 505.04 ± 0.43 [6] 352.48 ± 0.81 [6] 30.30 ± 1.06 [4] -
Table 2. Regression Coefficients of eq 14 for the Polymorphs of mHBA in Different Solvents
polymorph solvent A B C χ2 form I water 923.59 -25.928 0.05335 0.00003 methanol 333.25 -7.817 0.01473 0.00001 ethanol 555.74 -8.722 0.01568 0.00003 1-propanol 924.61 -11.541 0.02062 0.00003 ethyl acetate -26.86 -7.821 0.01655 0.00001 acetonitrile -1936.53 -0.591 0.00873 0.00017 form II water 1043.76 -26.105 0.05366 0.00050 ethyl acetate 1039.51 -14.287 0.02701 0.00002 acetonitrile 189.68 -14.473 0.03207 0.00003
The melting temperature Tm and associated enthalpy of fusion ΔHf (Tm) of each polymorph have
been determined. For form I, the process was straightforward. However, samples of crystallized form II consistently transformed into form I (partially or completely) prior to melting. After one melting – recrystallization cycle, melting occurred at a lower temperature with a lower enthalpy of fusion. Through FTIR spectroscopy the material with the lower melting point was confirmed to be form II. A possible explanation is that trace amounts of form I material from the crystallization was present in the original form II material, templating the transformation process, but that a recrystallization from the melt inside the pan resulted in pure form II material. The specific heat capacity of both polymorphs was determined in the temperature range -30–130 °C. A linear regression model was used (eq 15), and the coefficients k1 and k2 were determined by a least-squares fit of the data obtained at different
temperatures in 6 scans for each polymorph:
7
Figure 3. Solubility of mHBA in several solvents, from above: methanol (hollow triangles), ethanol
(hollow squares), 1-propanol (hollow circles), ethyl acetate (solid triangles), acetonitrile (solid squares) and water (solid circles) for form I (red) and form II (blue), with corresponding regression curves.
Melting data and the coefficients of eq 15 are given in Table 3. No attempts to determine the heat capacity of the melt or of the solid phases at higher temperatures were made because of material losses due to evaporation and sublimation. The uncertainty in the heat capacity determination can be approximately estimated through calculation of 95% confidence intervals of the regressed data at different temperatures; at 300 K the uncertainties in CP,I and CP,II are ±2.7% and ±1.1%, respectively,
while at 400 K the corresponding values are ±1.9% and ±1.3%.
Table 3. Melting Data Given With 95% Confidence Limits and Coefficients of eq 15 for Forms I
and II
Melting data Heat capacity coefficients
polymorph scans Tma [°C] ΔHf (T m) [kJmol-1] scans T-interval [K] k1 [Jmol-1K-2] k2 [Jmol-1K-1] form I 8 201.08 ± 0.14 35.83 ± 0.22 6 243–403 0.478 20.5 form II 9 194.34 ± 0.38 32.68 ± 0.42 6 243–403 0.505 15.2
a Extrapolated onset temperature.
The melting temperature of form II is lower than that of form I by 6.7 °C. In conjunction with solubility data, this shows that there is no transition in stability above room temperature. Since ΔHf
II <
ΔHfI, it can be surmised that the stability relationship is monotropic26. Nordström and Rasmuson
(2008)17 have described a method for calculating the activity of a solid phase as a function of
temperature using solubility and calorimetric data, based on the correlation in a range of different solvents between the solubility and its temperature dependence given by the van’t Hoff, or apparent, enthalpy of solution:
∆𝐻𝑠𝑜𝑙𝑛𝑣𝐻 = 𝑅𝑇2(𝜕 ln 𝑥
𝜕𝑇 )𝑒𝑞 (16)
This method was used to estimate the coefficients of eq 4 and the activity of form I of mHBA. Solubility data in six solvents were used, at nine temperatures from 10 °C to 50 °C (by 5 °C increments), where concentrations are sufficiently high to avoid the Henry’s law region where the correlation breaks down25: acetonitrile, ethyl acetate, acetic acid and methanol, using data from
8 ln xeq for the six solvents at five different temperatures, together with correlated second order
polynomials. Using an iterative approach17, minimizing an objective function given by the RMS of the
residuals at nine temperatures between the van’t Hoff enthalpy of solution obtained using the correlations in Figure 4 and the corresponding van’t Hoff enthalpy of an ideal solution, i.e. ΔHf
calculated by eq 7, the best set of parameters of eq 4 was obtained. Melting data in Table 3 was used.
Figure 4. The correlation between ΔHvH
soln and solubility at 10 °C (bottommost curve), 20 °C, 30
°C, 40 °C and 50 °C (topmost curve), for acetonitrile (triangles), acetic acid (crosses), ethyl acetate (plusses), methanol (squares), 1-propanol (circles) and ethanol (diamonds).
Because of a shortage of high-quality solubility data this method was not feasible for form II. Instead, ΔCP,II was calculated from ΔCP,I and the experimentally determined CP data for the two
polymorphs, extrapolated up to the melting point of form I. Together with melting data the thermodynamic properties of form II could then be calculated using eqs 5–8. In Figure 5 the experimental heat capacities of the two polymorphs are shown together with the calculated heat capacity of the supercooled melt. Figure 6 a) shows quantitatively how the free energy, enthalpy and entropy of fusion of each polymorph depend on temperature, and in Figure 6 b) the difference in the corresponding properties between the two polymorphs are shown. The coefficients of eq 4 are given in Table 4.
Figure 5. Heat capacity of form I (red, lower), form II (blue, middle), experimentally determined
(solid lines) and extrapolated to the melting points (dashed lines), and the calculated heat capacity of the pure liquid (green, upper dashed line).
Table 4. Coefficients of eq 4 for the Two Polymorphs
polymorph q [Jmol-1K-1] r [Jmol-1K-2]
form I 160.1 -0.421
9
Figure 6. a) Gibbs free energy of fusion of form I (red, upper) and form II (blue, lower); b) Gibbs
free energy of transformation (form II → form I), together with their enthalpic and entropic components, plotted against temperature from room temperature up to melting.
Estimating the errors associated with the calculated thermodynamic properties is by no means straightforward. The uncertainty in the estimation of ΔHf (T
m) averaged for the two polymorphs is
estimated to be 0.9%, and for form II there is the additional uncertainty from the experimental determination of CP (T) for each polymorph estimated to be between 2–3% at 300 K (95% confidence
limits). Furthermore, the thermodynamic analysis relies heavily on the validity and strength of the correlation between solubility and ΔHvHsoln, but the correlations obtained in six solvents at all
temperatures are very strong (R2 ≥ 0.99). Finally, our approximation of a linear function to describe ΔCP
is validated by the fact that residuals in activity at all the nine temperatures are <0.5%, showing insignificant systematic deviations with temperature17.
The calculated energy difference between the polymorphs is fairly small: the Gibbs free energy difference is only 0.87 kJ/mol at room temperature (298 K), with the curves converging somewhat with increasing temperature. The enthalpy difference is 1.20 kJ/mol at 298 K, increasing with increasing temperature. The entropic contribution to the free energy difference (TΔStr) amounts to only 0.35 kJ/mol
at 298 K, about a quarter of the magnitude of the enthalpy difference, and works in the opposite direction, favouring form II. At the melting temperature of the metastable form II (467.5 K), the corresponding values are 0.50 kJ/mol, 2.08 kJ/mol and 1.60 kJ/mol, respectively. The ratio of calculated solid-state activities is 1.4 at 298 K, decreasing to around 1.1 at Tm,II. This ratio may be
10 compared to the ratio of mole fraction solubilities, α, which, provided that the concentration dependence of the activity coefficients is small, should not be very different:
𝑎𝐼𝐼 𝑎𝐼 ≅
𝑥𝑒𝑞,𝐼𝐼
𝑥𝑒𝑞,𝐼 = 𝛼 (17)
At 298 K, the value of α in water is 1.37, in ethyl acetate 1.27, and in acetonitrile 1.25. In all the solvents, the estimated errors as well as variations with temperature are both small (on the order of 1%) in the temperature range 10–50 °C. It should thus be noted that there is a slight concentration dependence of the activity coefficients in these solvents. The absolute value of the activity coefficient, calculated using the solubility of form I at 50 °C, is around 0.4 in methanol, ethanol and 1-propanol, with a slightly higher value (0.7) in ethyl acetate, i.e. for these solvents mHBA solutions exhibit negative deviation from ideality (defined according to Raoult’s law), and solvent-solute interactions are more favourable in comparison with the respective pure liquid states. The activity coefficient is 2.5 in acetonitrile, indicating somewhat unfavourable solute-solvent interaction, but in water the value exceeds 19, a large positive deviation indicating a high excess free energy of mixing.
Nucleation experiments
Nine experimental series, each comprising two batches of 30 crystallization experiments, with different solvents and cooling rates, were carried out. The experimental details and results are summarized by series in Table 5. In the last columns, values of the average driving force at nucleation of the respective polymorphs, estimated through eq 9, are listed. As the solubility of form II could not be determined experimentally in ethanol or methanol, nor at temperatures above 20 °C in 1-propanol, it was estimated from the average value of α at low temperatures in 1-propanol (viz. 1.14). The rationale for using this value, apart from acknowledging the chemical resemblance, is that, since the solubility in the three alcohols is fairly similar, and higher by 1–2 orders of magnitude compared to the other solvents, the influence of the activity coefficient ratio should also be fairly similar. In Figure 7, the fraction of nucleations resulting in form I is shown for each experimental series, together with 95% confidence limits calculated with the Wilson method16 with no correction for continuity.
Table 5. Summary of Cooling Crystallization Experiments with Different Polymorphic Outcome,
the Average Metastable Zone Width with Respect to the Solubility of Form I, and the Average Values of RT ln s at Nucleation of Each Respective Polymorph, with 95% Confidence Limits
no. of nucl. exp. avg. [RT ln s]nucl [kJmol-1]
series no.
solvent -dT/dt [°C/h]
total form I form II concom. MZW [°C] form I form II 1 water 10 60 5 55 0 13.4 ± 0.1 1.50 ± 0.09 0.73 ± 0.01 2 “ 3 60 4 56 0 12.4 ± 0.2 1.32 ± 0.04 0.63 ± 0.02 3 methanol 10 59 24 34 1 18.0 ± 1.2 0.45 ± 0.05 0.24 ± 0.03 4 ethanol 10 60 43 14 3 22.8 ± 1.2 0.53 ± 0.03 0.33 ± 0.04 5 1-propanol 10 60 17 39 4 27.5 ± 1.0 0.64 ± 0.05 0.45 ± 0.01 6 ethyl acetate 10 60 0 59 1 34.6 ± 0.6 > 1.65 0.80 ± 0.02 7 “ 3 60 13 35 12 30.3 ± 0.5 1.20 ± 0.04 0.67 ± 0.02 8 acetonitrile 10 60 8 52 0 14.7 ± 1.1 0.37 ± 0.23 0.63 ± 0.03 9 “ 3 60 11 45 4 13.4 ± 0.6 0.79 ± 0.21 0.47 ± 0.12
11
Figure 7. The fraction of crystallizations resulting in form I with 95% confidence limits for the nine
experimental series.
In the analysis of the results, it is assumed that FTIR analysis of the filtered and dried crystals is a reliable method of identifying the nucleating polymorph. As shown in Figure 2, the FTIR spectra are quite distinct in the fingerprint region, particularly with respect to the presence or absence of a peak at ~1270 cm-1, which is important for the detection of concomitant nucleation. In order to minimize the risk of polymorphic transformation of form II into form I occurring after nucleation, the test tubes were removed as soon as a sufficient amount of crystal material had formed, and filtered immediately. Drying was conducted by evaporation in a ventilated fume hood at room temperature, and is estimated to require less than an hour, typically only a few minutes for the majority of samples. FTIR analyses were then performed within 24 h. In the dry state at ambient conditions, it is our experience that the metastable material in powder form does not undergo transformation to any discernible degree for periods of weeks or even months. Furthermore, in all evaluated solvents form II crystals remain untransformed for several hours at low temperatures – in most solvents for a sufficiently long time to allow solubility data to be collected. Accordingly, there should be little risk that any cases of form II nucleation were overlooked, and that if cases of concomitant nucleation were mistakenly assigned as either pure polymorph it should be a matter of trace amounts.
In acetonitrile, occasional test tubes would, soon after nucleation was observed, undergo a sudden change from a semi-translucent, weakly cloudy state into a thick, creamy white suspension. Invariably, if the material in test tubes containing the semi-translucent suspension was filtered and dried, the FTIR spectrum of form I was obtained. However, solutions which had transformed into a thick, white suspension resulted in the spectrum of form II. Based on observations of the nucleated test tubes prior to filtration, the hypothesis is that the supersaturation was not always consumed quickly enough by the nucleated form I crystals to prevent nucleation of form II. The metastable polymorph, once it had nucleated, tended to grow quite rapidly, resulting in classification of some samples as ostensibly pure form II rather than concomitant crystallization. Effort was taken to prevent nucleated tubes from remaining unfiltered for longer than necessary, but this was not enough to completely prevent this effect. Accordingly, in acetonitrile, the results with respect to nucleating polymorph must be treated as uncertain, with possibly erroneous values of RT ln snucl and underestimated form I fractions.
General Influence of Solvent and Cooling Rate on Nucleation
The results of all nucleation experiments of series 1–7 are shown in Figure 8 in the form of normalized cumulative distributions of nucleation events of each respective polymorph with increasing nucleation driving force.
12
Figure 8. Cumulative distributions of nucleation events of form I (red diamonds) and form II (blue circles) with increasing driving force, for
series 1–7. For each nucleation event the driving force with respect to both polymorphs is shown; the lower axis (red digits) gives RT ln s with respect to the stable form I and the upper axis (blue digits) with respect to form II. Vertical blue lines denote RT ln sII = 0.
13 The shapes of the distributions differ somewhat between the series, but overall they are fairly well approximated by the normal distribution function, in spite of any effects of overlap between the distributions of the two polymorphs. This means that the distributions can be justly described by mean values and confidence intervals as reported in Table 5. Notably, all distributions are fairly narrow, which is reflected in the confidence values of the mean. As seen in Figure 8 and Table 5, depending on solvent and cooling rate, there are differences in the metastable zone width, and in the distribution of nucleation events with thermodynamic driving force for nucleation. The overall average effect of a reduced cooling rate on the metastable zone was in all cases a reduction in the width. In terms of temperature, the reduction was 1.0 °C for water, 4.3 °C for ethyl acetate and 1.3 °C for acetonitrile. This clearly shows that nucleation is not very fast compared to the cooling rate; the moment when nucleation is observed depends not only on the level of supersaturation but also on the time of converting unstable clusters into crystal nuclei and/or the time for these to grow to detectable size.
The supersaturation driving force required for nucleation irrespective of polymorph decreases in the order: ethyl acetate > water > acetonitrile > 1-propanol > ethanol > methanol, with no apparent correlation to any of the various solvent properties relating to polarity or hydrogen bonding ability, e.g. dielectric constant, Reichardt’s polarity parameter27 E
TN or Hildebrand/Hansen solubility parameters.
However, as shown in Figure 9 a), there is some correlation to the solubility (mol/m3) of form I at 50
°C, which increases in the order: water < acetonitrile < ethyl acetate < 1-propanol < ethanol < methanol. Notably, the correlation to the mole fraction solubility is worse. The rate of nucleation is expected to increase with decreasing interfacial energy (eq 13), and it may be reasonable to expect the interfacial energy to be inversely related to the solubility for a solute in different solvents, in analogy with the case of different solutes in aqueous solution28. Accordingly, the interfacial energy term will contribute to a
decreased supersaturation driving force required for nucleation in the alcohols where solubility is high and an increased driving force in water where solubility is low. Ethyl acetate and acetonitrile rank in between these solvents in terms of solubility, and this is consistent as regards acetonitrile, but in ethyl acetate the metastable zone should be much narrower.
Figure 9. Average values of RT ln s at nucleation plotted against a) the molar solubility of form I at
50 °C and b) ηVm,solvent/C√(T3Msolvent) for the experiments at a cooling rate of 10 °C/h in five solvents for
form I (red, upper) and form II (blue, lower); methanol, ethanol, 1-propanol, ethyl acetate and water. Ethyl acetate is shown with hollow symbols, error bars show 95% confidence limits, and in b) data in water, methanol, ethanol and 1-propanol are correlated by a straight line.
The solute concentration also appears explicitly in the pre-exponential factor of eq 13, together with several other physical parameters. In Figure 9 b), the average driving force at nucleation is plotted against a grouping of parameters from the pre-exponential factor containing the molar mass and
14 volume of the solvent and the solution viscosity, here approximated by that of the solvent at Tnucl29. The
data in water and the three alcohols is fairly well described by a straight line for each polymorph in Figure 9 b), suggesting a relationship to the kinetics of molecular motion and collisions in solution captured by the attachment frequency, f* (eq 10). In water, the low solute concentration will decrease the
frequency of collisions, and the high viscosity and low solvent molar mass will reduce the diffusivity, slowing down nucleation. The alcohols exhibit a higher solute concentration and a lower viscosity, and a lower driving force is required for nucleation. Among the alcohols, the driving force required for nucleation of either polymorph increases with increasing solvent molar mass, aliphatic chain length and non-polar element, which correlates to decreasing solubility (in mol/m3) from methanol via ethanol to
1-propanol, and to decreasing concentration of nucleation sites because of increasing solvent molar volume. It seems that differences in solvent physical properties can contribute to an explanation of why nucleation is comparatively slow in 1-propanol and fast in methanol. However, given the physical properties of ethyl acetate, the driving force required for nucleation in this solvent is very high, which points to effects of solvent-solute interaction which are not directly captured by eqs 10–13. Since ethyl acetate is a non-HBD solvent its molecules cannot hydrogen-bond with each other, and as a result all ethyl acetate molecules are available for hydrogen bonding with the –OH and –COOH groups of the mHBA molecules. Such energetically favourable solvation could explain a higher nucleation energy barrier.
Polymorphic outcome
None of the experimental series resulted in an outcome of 100% of the solution samples crystallizing as one particular polymorph, in spite of varying the cooling rate by more than a factor 3 and performing crystallizations in a chemically diverse range of solvents. If we consider the full range of data in Figure 8, we can see that the distributions of nucleation events of the two polymorphs overlap to a large extent in the alcohols, and almost entirely in water. This in turn points to a significant overlap of the occurrence domains of the polymorphs, and clearly reveals the randomness of the nucleation process. In Figure 10, the estimated average driving force required for nucleation of the stable form I is compared to that of form II (data from Table 5). In ethyl acetate solution at a cooling rate of 10 °C/h (series 6), the average value of RT ln sI is marked as exceeding the value of RT ln sI at the temperature when the last
tube nucleated, viz. 1.65 kJ/mol. In all solvents under all conditions, nucleation of the metastable polymorph is kinetically favoured, which is in agreement with work reported by He et al30. In ethyl
acetate and water formation of form II dominates strongly in spite of a lower supersaturation driving force, while the fractions are more even in the alcohols. There appears to be a general tendency for form II to be favoured over form I in solvents where nucleation overall is hampered. In all solvents the required driving force for nucleation of the stable polymorph is about twice that of form II, but the difference in absolute terms amounts to ≥0.8 kJ/mol in water and ethyl acetate but only about 0.2 kJ/mol in the three alcohols.
An analysis of the driving force required for nucleation suggests that slower cooling primarily affects the metastable zone width of form I. As can be seen in Figure 10, in water a reduction in the cooling rate from 10 to 3 °C/h only had a small effect on the supersaturation required for nucleation of the two polymorphs, and there was no statistically established change in the fractions of nucleating polymorphs. In ethyl acetate, however, the reduction in cooling rate led to a substantial decrease in the supersaturation required for nucleation of form I, shifting the balance in the direction of thermodynamic control, and this resulted in the fraction of pure form II nucleations dropping by 40 percentage points.
15
Figure 10. Average values of RT ln s at nucleation of the respective polymorph for series 1–7. Box
edges mark upper and lower 95% confidence limits centred on the average. Solid-line boxes represent a cooling rate of 10 °C/h and dashed-line boxes 3 °C/h. The diagonal line represents the equality RT ln sI
= RT ln sII.
Several mechanisms have been identified by which a solvent may influence the polymorphic outcome at the molecular level4, 7. The main structural feature which distinguishes the two mHBA
polymorphs is the centrosymmetric carboxylic acid dimer, present only in the structure of form I. It may be speculated that in aqueous solution, dissociation of the carboxyl group and the formation of strong, static solvation shells around the solute molecules with water molecules strongly associated to the carboxyl groups will suppress dimerization and hamper nucleation of form I. In the other solvents, however, it appears that the solvent influence on the polymorphic outcome is more complex. It is well known that supersaturation usually is an important factor for the polymorphic outcome, as is – under transient conditions – its rate of generation. The solubility and its temperature dependence differ in different solvents, but rarely is this fact properly accounted for in comparisons of the influence of the solvent. In the following, this aspect is developed in some depth, with no claim that structural aspects on the molecular level could not also be important for the interpretation of the results.
In Figure 11, the driving force at each detected nucleation event for the respective polymorphs is plotted against the gradual increase in undercooling relative to the starting temperature 50 °C (which is also the saturation temperature of form I), ΔTuc = (Tsat,I -T). Since the rate of cooling is constant, the
x-axis is directly proportional to the elapsed time. The nucleation events of the two polymorphs are plotted on the respective curves. Each experiment starts at the right edge at saturation with respect to form I, and the solid lines show how the supersaturation with respect to each polymorph increases as the solution temperature is reduced. Notably, the rate of generation of supersaturation is fairly constant, irrespective of polymorph. During cooling, the solution initially becomes supersaturated with respect to the stable form I, and only later also with respect to the metastable form II, resulting in a time window, Δtsat, during which only the stable polymorph is thermodynamically allowed to nucleate, and given
sufficient time it will. However, as the solution is cooled further and becomes supersaturated also with respect to the kinetically favoured form II the window of opportunity for form I to nucleate gradually passes. The duration of this time window depends on the cooling rate, the difference in solubility between the two polymorphs, and the slope of the solubility curves with respect to temperature.
In Table 6 is given the slopes of the curves in Figure 11, the corresponding rates of supersaturation generation, and the temperature and time differences between the points when the solution becomes saturated with respect to each respective polymorph. Obviously, the value of Δtsat depends strongly on
the solvent. At a cooling rate of 10 °C/h a solution of ethanol will be undersaturated with respect to form II for ~9 min longer than solutions of methanol or 1-propanol. Since there is no significant difference in the driving force required for nucleation of the two polymorphs between these solvents,
16 this larger time window could partly explain the statistically established higher fraction of form I nucleations obtained in ethanol. In Figure 12, the fraction of nucleations resulting in form I is plotted against Δtsat for each solvent at equal cooling rate. For the three alcohols and water, there is a trend of
increasing fraction of form I with increasing Δtsat.
For different solvents at constant temperature we expect a correlation between the solubility and its temperature derivative25. Hence, when cooling solutions of different solvents at a constant rate, we
expect a correlation between the rate of generation of supersaturation and the solubility. In Figure 13, the average rate of change of RT ln s is plotted against the mole fraction solubility at 50 °C for form I in six solvents, indeed showing an excellent linear correlation (R2 = 0.99). A similar correlation is found
for form II. Since the curves of the two polymorphs in Figure 11 are essentially parallel in all solvents, it follows that we can expect a correlation of increasing Δtsat with increasing solubility, as schematically
illustrated in Figure 14. At point A, the solution is saturated with respect to form I. In the lower solubility solvent (solid lines) the solution becomes saturated with respect to form II (blue curve) at point B. In the higher solubility solvent (dashed lines) the dependence of supersaturation on temperature is weaker and this event occurs at a lower temperature, point C. As shown in Figures 12 and 13 (green curve), in water and the alcohols the results indeed indicate that with increasing solubility follows an increasing Δtsat at constant cooling rate, resulting in an increased propensity for nucleation of the stable
polymorph. Ethyl acetate is a clear exception from this behaviour.
Table 6. Temperature and Time Derivative of Supersaturation Driving Force for Nucleation of the
Two Polymorphs, and the Difference in Temperature and Process Time from Saturation of Form I Until Saturation of Form II
Δ(RT ln s)/ΔΔTuc Δ(RT ln s)/Δt
series no. solvent [JK-1mol-1] [Jmin-1mol-1] ΔTsat (I-II) [°C] Δtsat (I-II) [min] form I form II form I form II
1 water 102 102 17.0 17.0 6.8 41 2 5.1 5.1 136 3 methanol 26 27 4.3 4.5 11.6 70 4 ethanol 23 24 3.8 4.0 13.1 79 5 1-propanol 25 26 4.2 4.3 11.6 70 6 ethyl acetate 40 39 6.7 6.5 12.9 77 7 2.0 2.0 258 8 acetonitrile 70 73 11.7 12.2 7.9 47 9 3.5 3.7 158
17
Figure 11. Plots of RT ln s (solid lines, dashed if based on estimated solubility, dotted if negative)
together with the nucleation events (circles) for form I (red, upper) and form II (blue, lower) in various solvents, for the cooling rate 10 °C/h, with the temperature of undercooling on the abscissa.
18
Figure 12. The fraction of crystallizations (10 °C/h) resulting in form I plotted against Δtsat for five
solvents, with error bars showing 95% confidence limits.
Figure 13. Average rate of increase in RT ln sI (left axis, purple circles) and Δtsat (right axis, green
diamonds) for a cooling rate of 10°C/h plotted against mole fraction solubility at 50 °C, with corresponding linear correlation, in the six solvents.
Figure 14. Schematic representation of the influence of solvent on the slope of supersaturation vs.
temperature curves (cf. Figure 11). Red represents stable polymorph and blue metastable, solid and dashed lines represents two different solvents.
19
C
ONCLUSIONSFrom experimental solubility and melting data it is concluded that the two polymorphs of m-hydroxybenzoic acid are monotropically related. The calculated free energy difference between the polymorphs is 0.87 kJ/mol at 298 K, decreasing to 0.50 kJ/mol at 467.5 K, the melting temperature of form II. The difference in enthalpy is 1.20 kJ/mol at 298 K, increasing to 2.08 kJ/mol at Tm,II. The ratio
of calculated solid-state activities between forms II and I is 1.4 at 298 K, decreasing to 1.1 at Tm,II. The
corresponding ratio of mole fraction solubilities at 298 K is approximately 1.37 in water, 1.26 in ethyl acetate and 1.25 in acetonitrile, pointing to a slight concentration dependence of the activity coefficient.
The nucleation results show that there is a significant stochastic variation in both nucleation temperature and nucleating polymorph. The polymorphic outcome is shown to depend on the solvent. The metastable form II is kinetically favoured in all the solvents, but to a varying degree, and in no case was an outcome of 100% of either polymorph obtained. In ethyl acetate and water nucleation of the metastable form II strongly dominates, while in propanol, methanol and ethanol the fraction of nucleation of form I becomes increasingly higher. For both polymorphs, the average thermodynamic driving force required for nucleation decreases in the order: ethyl acetate > water > acetonitrile > 1-propanol > ethanol > methanol. A correlation is found between decreasing driving force at nucleation and decreasing solvent viscosity and increasing solubility, parameters that are captured by the pre-exponential factor in the classical nucleation rate equation.
The work shows that a proper analysis of how the driving force for nucleation of each polymorph develops during the cooling crystallization is helpful in explaining why nucleation of the stable form is promoted in solvents where the solubility is high.
A
CKNOWLEDGEMENTSThe financial support of the Swedish Research Council and the Science Foundation Ireland is gratefully acknowledged.
20
N
OTATIONA i) Exponential coefficient in nucleation rate equation ii) Solubility regression coefficient
a Activity
B Solubility regression coefficient
C i) Concentration
ii) Solubility regression coefficient
CP Isobaric specific heat capacity
D Molar diffusion coefficient
f Molecular attachment frequency
G Gibbs free energy
H Enthalpy
J Steady-state nucleation rate
k1,2 Heat capacity regression coefficients
M Molar mass
q ΔCP correlation coefficient
R i) Gas constant ii) Pearson’s R r i) Nucleus radius
ii) ΔCP correlation coefficient
S Entropy
s Supersaturation ratio
T Temperature
t Time
Vm Molar volume
x Solute mole fraction
Z Zeldovich factor
α Mole fraction solubility ratio (form II : form I)
γ Activity coefficient η Solution viscosity κ Sticking coefficient μ Chemical potential σ Interfacial energy Superscripts, subscripts eq Equilibrium f Fusion I, II Form I, form II L Liquid m Melting ns Nucleation sites S Solid sat Saturation soln Solution tr Transformation uc Undercooling
vH van’t Hoff (enthalpy)
21
R
EFERENCES(1) Byrn, S.; Pfeiffer, R.; Ganey, M.; Hoiberg, C.; Poochikian, G. Pharm. Res. 1995, 12, 945.
(2) Lee, A. Y.; Lee, I. S.; Myerson, A. S. Chem. Eng. Technol. 2006, 29, 281.
(3) Davey, R. J.; Blagden, N.; Righini, S.; Alison, H.; Quayle, M. J.; Fuller, S. Cryst. Growth Des. 2001, 1, 59.
(4) Hamad, S.; Moon, C.; Catlow, C. R. A.; Hulme, A. T.; Price, S. L. J. Phys. Chem. 2006, B110, 3323.
(5) Parveen, S.; Davey, R. J.; Dent, G.; Pritchard, R. G. Chem. Commun. 2005, 1531.
(6) Towler, C. S.; Davey, R. J.; Lancaster, R. W.; Price, C. J. J. Am. Chem. Soc. 2004, 126, 13347.
(7) Han, G.; Poornachary, S. K.; Chow, P. S.; Tan, R. B. H. Cryst. Growth Des. 2010, 10, 4883.
(8) Jiang, S.; Jansens, P. J.; ter Horst, J. H. Cryst. Growth Des. 2010, 10, 2123.
(9) Svärd, M.; Nordström, F. L.; Jasnobulka, T.; Rasmuson, Å. C. Cryst. Growth Des. 2009, 10, 195.
(10) Williams, P. A.; Hughes, C. E.; Lim, G. K.; Kariuki, B. M.; Harris, K. D. M. Cryst. Growth Des. 2012, 12, 3104.
(11) Nordström, F. L.; Rasmuson, Å. C. J. Chem. Eng. Data 2006, 51, 1668.
(12) Nordström, F. L.; Rasmuson, Å. C. Eur. J. Pharm. Sci. 2006, 28, 377.
(13) Nordström, F. L.; Rasmuson, Å. C. J. Pharm. Sci. 2006, 95, 748.
(14) Kariuki, B. M.; Bauer, C. L.; Harris, K. D. M.; Teat, S. J. Angew. Chem. Int. Ed. 2000, 39, 4485.
(15) Gridunova, G. V.; Furmanova, N. G.; Struchkov, Y. T.; Ezhkova, Z. I.; Grigoreva, L. P.; Chayanov, B. A.
Kristallografiya 1982, 27, 267.
(16) Nordström, F. L.; Svärd, M.; Malmberg, B.; Rasmuson, Å. C. Cryst. Growth Des. 2012, 12, 4340.
(17) Nordström, F. L.; Rasmuson, Å. C. J. Chem. Thermodyn. 2008, 40, 1684.
(18) Volmer, M. Kinetik der Phasenbildung; Steinkopff: Dresden, 1939.
(19) Becker, R.; Döring, W. Ann. Phys. 1935, 24, 719.
(20) Zeldovich, Y. B. Acta Physicochim. URSS 1943, 18, 1.
(21) Kashchiev, D.; van Rosmalen, G. M. Cryst. Res. Technol. 2003, 38, 555.
(22) Walton, A. G. Nucleation in liquids and solids. In Nucleation, Zettlemoyer, A. C., Ed. Marcel Dekker: New York,
1969.
(23) Wilke, C. R.; Chang, P. Am. Inst. Chem. Eng. J. 1955, 1, 264.
(24) Nývlt, J. Likely grounds of the thermal history of solutions. In Proceedings of the 9th Symposium of Industrial
Crystallization; Jancic, S. J.; de Jong, E. J., Eds.; Elsevier, 1984.
(25) Nordström, F. L.; Rasmuson, Å. C. Eur. J. Pharm. Sci. 2009, 36, 330.
(26) Burger, A.; Ramberger, R. Microchim. Acta 1979, 72, 259.
(27) Reichardt, C. Solvents and solvent effects in organic chemistry; Wiley-VCH: Weinheim, 2003.
(28) Bennema, P.; Söhnel, O. J. Cryst. Growth 1990, 102, 547.
(29) Lide, D. R., Handbook of chemistry and physics, 73rd ed.; CRC: Boca Raton, 1992.
